What is distinctive about the way Novak Djokovic or Roger Federer serves? What makes serves similar and what makes them different?

These questions refer to the 'playing style' of each player. First serves alone contribute to top male tennis players winning more than 80% of the points in a game.

(Johnson & McHugh, 2006)

A sneak peak…

2000 serves from the 2016 Australian Open Tournament.

The serves described by 2 arcs, a function for the X, Y, Z position of the ball across time.

In addition to server, receiver, speed, starting position, net clearance, side, winner or fault, height of bounce, angle change, …

The first questions we naturally asked is what are the types of serves a tennis player can do? Coaching literature defines a few types of serves:

• Flat serve
• Top spin serve
• Slice serve
• Kick serve

To change the serve type a player can control the ball toss and the way the racquet makes impact with the ball.

We would like to know if the serve data from the Australian Open reflects these types of serves, and how players utilise different serves.

We don't have a "serve type", need to guess it from the data based on the arc descriptions.

These variables are used:

• Start position: x, y, z
• Speed
• Height off the bounce
• Net clearance
• Location of the bounce in the service box: x, y
• Angle change

The variables were all scaled to mean 0 and variance 1, so that each contribute to the clustering equally. Data also transformed into principal components, first four used. More on this later.

One serve start.x position didn't get flipped properly, a handful of serve starts are actually baseline return positions.

• Euclidean distance between serves is used
• Ward's linkage

## 
##   1   2   3   4   5 
## 429 470 111 307 283

• Dendrogram would suggest 2, 4, 5, … clusters
• Cluster stats provide somewhat corroborating: 4, 6, 12
• Finer clustering might give more interesting breakdown of serving styles

Examine a low-dimensional representation.

Most clusters defined in PC1 and PC2, except 3 and 7.

Clusters 3, 7 contain unusal serves.

• Clusters 1, 2, 10 are fast, flat serves
• Cluster 9 has slow, high bounce, high angle, long, deuce side serves; cluster 3 (of outliers) are similar serves, from both deuce and ad sides
• Cluster 4, 5, 12 are similarly a bit slower, more bounce, not as much angle change, with cluster 5 tending to be hit deeper into the ad court
• Clusters 6, 7, 8, 11 are fast, not much bounce but some with negative angle change.

• Raonic tends to do serve type 10 on his first serve, and serve type 7 on his second serve
• Serve type 9 is mainly Djokovic, Ferrer, Nishikori and Monfils on their second serve

• Djokovic consistency, hits different serves from same spot.
• Raonic appears to toss slightly different for different serves.

Angle change measures change in trajectory at the bounce. The negative values arise from angle change calculation.

Mostly serves by Murray!

##       server  receiver
## 1    KYRGIOS   BERDYCH
## 2     MURRAY     SOUSA
## 3      SIMON  DJOKOVIC
## 4   DJOKOVIC     SIMON
## 5      ISNER    FERRER
## 6    MONFILS KUZNETSOV
## 7    MONFILS KUZNETSOV
## 8     MURRAY     TOMIC
## 9  NISHIKORI  DJOKOVIC
## 10    MURRAY    FERRER
## 11   MONFILS    RAONIC
## 12    MURRAY    RAONIC
## 13    MURRAY    RAONIC
## 14    MURRAY    RAONIC

• The cluster analysis on the serve data essentially corroborates common knowledge about serve types, flat, top spin, slice, kick serves, but enables a finer dissection of serving style.

• Other clustering methods may produce some differences results, but we think the clusters defined are fairly robust

• Accurate spin variables to capture axis rotation and amount of spin on the ball
• Functional based clustering may be an option to observe serve curvature. Should location be considered for "playing style", is a standardised impact point better?
• Combine serve type, with serve strategy. Do players serve differently to different opponents? Or do they stick a dominant strategy?